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A proof of the trace theorem of Sobolev spaces
on Lipschitz domains

Author: Zhonghai Ding
Journal: Proc. Amer. Math. Soc. 124 (1996), 591-600
MSC (1991): Primary 46E35
MathSciNet review: 1301021
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Abstract: A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on $H^{s}(\partial\Omega)$. It is proved that the trace operator is a linear bounded operator from $H^{s}(\Omega)$ to $H^{s-\frac{1}{2}}(\partial\Omega)$ for $\frac{1}{2}<s<\frac{3}{2}$.

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  • 1 R. A. Adams, Sobolev Spaces, Academic Press, New York, 1978.MR 56:9247
  • 2 M. Costabel, Boundary integral operators on Lipschitz domains: elementary results, SIAM J. Math. Anal. 19 (1988), 613--626.MR 89h:35090
  • 3 Z. Ding and J. Zhou, Constrained LQR problems governed by the potential equation on Lipschitz domain with point observations, J. Math. Pures Appl. 74 (1995), 317--344.
  • 4 E. Gagliardo, Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Ren. Sem. Mat. Univ. Padova 27 (1957), 284--305.MR 21:1525
  • 5 P. Grisvard, Elliptic problems in nonsmooth domains, Pitman Advanced Publishing Program, Boston, 1985.MR 86m:35044
  • 6 D. S. Jerison and C. E. Kenig, Boundary value problems on Lipschitz domains, in Studies in Partial Differential Equations (W. Littmann, ed.), MAA Studies in Math., vol. 23, Math. Assoc. of America, 1982, pp. 1--68.MR 85f:35057
  • 7 C. E. Kenig, Recent progress on boundary-value problems on Lipschitz domains, Proc. Sympos. Pure Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 175--205.MR 87e:35029
  • 8 J. L. Lions and E. Magenes, Nonhomogeneous boundary value problems and applications, vol. 1, Springer-Verlag, New York, 1972.MR 50:2670
  • 9 G.Verchota, Layer potentials and regularity for the Dirichlet problems for Laplace's equation in Lipschitz domains, J. Funct. Anal. 59 (1984), 572--611.MR 86e:35038

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Additional Information

Zhonghai Ding
Affiliation: Department of Mathematics Texas A&M University College Station, Texas 77843
Address at time of publication: Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada 89154

Keywords: Sobolev spaces, Lipschitz domains, trace theorem
Received by editor(s): September 15, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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